D. Umehara et T. Uyematsu, ONE-POINT ALGEBRAIC GEOMETRIC CODES FROM ARTIN-SCHREIER EXTENSIONS OFHERMITIAN FUNCTION-FIELDS, IEICE transactions on fundamentals of electronics, communications and computer science, E81A(10), 1998, pp. 2025-2031
Citations number
8
Categorie Soggetti
Engineering, Eletrical & Electronic","Computer Science Hardware & Architecture","Computer Science Information Systems
Recently, Garcia and Stichtenoth proposed sequences of algebraic funct
ion fields with finite constant fields such that their sequences attai
n the Drinfeld-Vladut bound. In the sequences, the third algebraic fun
ction fields are Artin-Schreier extensions of Hermitian function field
s. On the other hand, Miura presented powerful tools to construct one-
point algebraic geometric (AG) codes from algebraic function fields. I
n this paper, we clarify rational functions of the third algebraic fun
ction fields which correspond to generators of semigroup of nongaps at
a specific place of degree one. Consequently, we show generator matri
ces of the one-point AG codes with respect to the third algebraic func
tion fields for any dimension by using rational functions of monomial
type and rational points.